Continuous polynomial local functionals on convex functions admit integral representations via a finite family of polynomials, obtained by approximating from a classified dense subspace of smooth functionals using Goodey-Weil distributions.
Hadwiger,Vorlesungen ¨ uber Inhalt, Oberfl¨ ache und Isoperimetrie, Springer, Berlin- G¨ ottingen-Heidelberg
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Integral representation of polynomial local functionals on convex functions
Continuous polynomial local functionals on convex functions admit integral representations via a finite family of polynomials, obtained by approximating from a classified dense subspace of smooth functionals using Goodey-Weil distributions.